Question
Download Solution PDFIf sec A + tan A = 5,then sin A is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sec A + tan A = 5
Concept used:
If sec A + tan A = x then,
⇒ sec A - tan A = 1/x
Formula used:
Sin θ = P/H ; sec θ = H/B ; tan θ = P/B
Pythagorean theorem:
H2 = P2 + B2
Where, H = hypotenuse ; P = perpendicular ; B = base
Calculation:
⇒ sec A + tan A = 5 ------- (1)
then,
⇒ sec A - tan A = 1/5 -------- (2)
Adding the eq.(1) and (2)
⇒ Sec A + tan A + sec A - tan A = 5 + (1/5)
⇒ 2 × sec A = 26/5
⇒ sec A = 13/5 = H/B
By Pythagorean theorem:
⇒ H2 = P2 + B2
⇒ (13)2 = P2 + 52
⇒ P2 = 169 - 25 = 144
⇒ P = √144 = 12
Sin A = P/H = 12/13
∴ The correct answer is 12/13.
Last updated on Jun 13, 2025
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